bv_cvxbook_extra_exercises

# m with ai rnn and bi rn consider the problem of

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ebsite and put it in your Matlab path before the default version (which has a bug). 7.14 Isoperimetric problem. We consider the problem of choosing a curve in a two-dimensional plane that encloses as much area as possible between itself and the x-axis, subject to constraints. For simplicity we will consider only curves of the form C = {(x, y ) | y = f (x)}, where f : [0, a] → R. This assumes that for each x-value, there can only be a single y -value, which need not be the case for general curves. We require that at the end points (which are given), the 69 curve returns to the x-axis, so f (0) = 0, and f (a) = 0. In addition, the length of the curve cannot exceed a budget L, so we must have a 0 1 + f ′ (x)2 dx ≤ L. The objective is the area enclosed, which is given by a f (x) dx. 0 To pose this as a ﬁnite dimensional optimization problem, we discretize over the x-values. Specifically, we take xi = h(i − 1), i = 1, . . . , N + 1, where h = a/N is the discretization step size, and we let yi = f (xi ). Thus our objective becomes N yi , h i=1 and our constra...
View Full Document

## This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at Berkeley.

Ask a homework question - tutors are online